In DESPERATE NEED OF HELP!!!

An object of mass m = 10 kg and speed v = 2 m/s collides head on with a second object of mass m = 5 kg which has a speed v = 1 m/s. The objects stick together. There are no external forces on the two objects (note the given "v"s are the speeds, not the velocities).

What is the final speed of the stuck-together masses?

(Fill in the blank): The final kinetic energy of the stuck together masses is _____ the sum of the initial kinetic energies of the two objects.
(A. equal to, B. less than, C. greater than?)

a. M1*V1 + M2*V2 = M1*V + M2*V.

10*2 - 5*1 = 10V + 5V. V = ?.

b. KE2 = 0.5M1*V^2 + 0.5M2*V^2. =
KE after collision.

c. KE1 = 0.5M1*V1^2 - 0.5M2*V2 = KE before collision.

To determine the final speed of the stuck-together masses, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.

The momentum of an object can be calculated by multiplying its mass by its velocity. Let's denote the mass of the first object as m1, its initial velocity as v1, the mass of the second object as m2, and its initial velocity as v2.

Given:
m1 = 10 kg,
v1 = 2 m/s,
m2 = 5 kg,
v2 = 1 m/s.

Conservation of momentum equation:
(m1 * v1) + (m2 * v2) = (m1 + m2) * vf,
where vf is the final velocity of the stuck-together masses.

Substituting the given values, we get:
(10 kg * 2 m/s) + (5 kg * 1 m/s) = (10 kg + 5 kg) * vf,
20 kg m/s + 5 kg m/s = 15 kg * vf,
25 kg m/s = 15 kg * vf.

Now, we can solve for vf:
vf = (25 kg m/s) / (15 kg),
vf = 5/3 m/s.

Therefore, the final speed of the stuck-together masses is 5/3 m/s.

Now let's determine the final kinetic energy of the stuck-together masses. Kinetic energy is given by the formula KE = 0.5 * mass * velocity^2.

The initial kinetic energy of an object is given by:
KE_initial = 0.5 * mass * initial velocity^2.

The sum of the initial kinetic energies of the two objects would be:
KE_initial_total = KE_initial1 + KE_initial2.

To find the final kinetic energy of the stuck-together masses, we need to calculate the final mass and final velocity, and then use the formula:
KE_final = 0.5 * mass_final * velocity_final^2.

Given that the two objects stick together, the final mass would be the sum of the masses:
mass_final = mass1 + mass2.

And the final velocity is equal to the final speed we calculated earlier:
velocity_final = vf.

Now we can substitute these values into the formula to find the final kinetic energy:
KE_final = 0.5 * (mass_final) * (velocity_final)^2.

Comparing the sum of the initial kinetic energies (KE_initial_total) to the final kinetic energy (KE_final), we can determine whether it is greater than, less than, or equal to the sum of initial kinetic energies.

Now you can solve the problem by plugging in the numbers and performing the necessary calculations. Let me know if you need any further assistance!